Instruction for performing a pseudorandom number seed operation

ABSTRACT

A machine instruction is provided that includes an opcode field to provide an opcode, the opcode to identify a perform pseudorandom number operation, and a register field to be used to identify a register, the register to specify a location in memory of a second operand to be used. The machine instruction is executed, and execution includes obtaining a modifier field of a register associated with the machine instruction; based on the modifier field having a first value, performing a deterministic pseudorandom number seed operation, which includes obtaining seed material based on information stored in the second operand; using a 512 bit secure hash technique and the seed material to provide one or more seed values; and storing the one or more seed values in a parameter block.

BACKGROUND

One or more aspects relate, in general, to processing within a computingenvironment, and in particular, to processing associated with generatingpseudorandom numbers to be used in computer applications or other typesof applications.

Pseudorandom numbers are numbers that appear random, but are not trulyrandom. They are numbers generated by a deterministic computationalprocess that provides statistically random numbers. Since the numbersare produced by a deterministic process, a given sequence of numbers canbe reproduced at a later date, if the starting point is known. That is,given a particular function and seed value, the same sequence of numbersis generated by the function.

Pseudorandom numbers are used in numerous computer applications, such assimulation, cryptography, and procedural generation, as examples.Various implementations exist to generate pseudorandom numbers that canbe used in these applications. These implementations include, forexample, library subroutines, as well as a limited function of theCipher Message with Chaining instruction available on some processors,such as IBM® z/Architecture capable processors.

BRIEF SUMMARY

Shortcomings of the prior art are overcome and advantages are providedthrough the provision of a computer program product for executing amachine instruction. The computer program product includes, forinstance, a computer readable storage medium readable by a processingcircuit and storing instructions for execution by the processing circuitfor performing a method. The method includes, for instance, obtaining,by a processor, a machine instruction for execution, the machineinstruction being defined for computer execution according to a computerarchitecture, the machine instruction including: an opcode field toprovide an opcode, the opcode to identify a perform pseudorandom numberoperation; and a register field to be used to identify a register, theregister to specify a location in memory of a second operand to be usedby the machine instruction; and executing the machine instruction, theexecuting including: obtaining a modifier (M) field of a registerassociated with the machine instruction; based on the M field having afirst value, performing a deterministic pseudorandom number seedoperation, the deterministic pseudorandom number seed operationincluding: obtaining seed material based on information stored in thesecond operand; using a 512 bit secure hash technique and the seedmaterial to provide one or more seed values; and storing the one or moreseed values in a parameter block associated with the machineinstruction.

Methods and systems relating to one or more aspects are also describedand claimed herein. Further, services relating to one or more aspectsare also described and may be claimed herein.

Additional features and advantages are realized through the techniquesof one or more aspects. Other embodiments and aspects are described indetail herein and are considered a part of the claims.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

One or more aspects are particularly pointed out and distinctly claimedas examples in the claims at the conclusion of the specification. Theforegoing and other objects, features, and advantages are apparent fromthe following detailed description taken in conjunction with theaccompanying drawings in which:

FIG. 1A depicts one example of a computing environment to incorporateand use one or more aspects;

FIG. 1B depicts further details of the processor of FIG. 1A;

FIG. 2A depicts another example of a computing environment toincorporate and use one or more aspects;

FIG. 2B depicts further details of the memory of FIG. 2A;

FIG. 3A depicts one embodiment of a format of a Perform PseudorandomNumber Operation instruction;

FIG. 3B depicts one example of the contents of general register 0 (GR0)to be used by the Perform Pseudorandom Number Operation instruction ofFIG. 3A;

FIG. 3C depicts one example of the contents of general register 1 (GR1)to be used by the Perform Pseudorandom Number Operation instruction ofFIG. 3A;

FIG. 3D depicts one example of the contents of a register R₁ to be usedin one aspect by the Perform Pseudorandom Number Operation instructionof FIG. 3A;

FIG. 3E depicts one example of the contents of a register R₁+1 to beused in one aspect by the Perform Pseudorandom Number Operationinstruction of FIG. 3A;

FIG. 3F depicts one example of the contents of a register R₂ to be usedin one aspect by the Perform Pseudorandom Number Operation instructionof FIG. 3A;

FIG. 3G depicts one example of the contents of a register R₂+1 to beused in one aspect by the Perform Pseudorandom Number Operationinstruction of FIG. 3A;

FIG. 3H depicts one example of processing associated with a functioncode specified by the Perform Pseudorandom Number Operation instructionof FIG. 3A;

FIG. 3I depicts one example of processing associated with checking amodifier indicator specified by the Perform Pseudorandom NumberOperation instruction of FIG. 3A;

FIG. 4A depicts one example of the format of a parameter block for useby a Perform Pseudorandom Number Operation instruction having a functioncode of 0;

FIG. 4B depicts one embodiment of the format of a parameter block foruse by a Perform Pseudorandom Number Operation instruction having afunction code of 3;

FIG. 5A depicts one embodiment of the formation of seed material for aninstantiation operation;

FIG. 5B depicts one embodiment of the formation of seed material for areseed operation;

FIG. 6 depicts one embodiment of the logic to generate V_(new);

FIG. 7 depicts one example of the logic to generate C_(new);

FIG. 8A depicts one embodiment of the logic to generate pseudorandomnumbers;

FIG. 8B depicts one example of creating hash values for use ingenerating pseudorandom numbers;

FIG. 9 depicts one embodiment of the logic to update a parameter blockbased on normal completion of a pseudorandom number generationoperation;

FIG. 10 depicts one embodiment of a computer program productincorporating one or more aspects;

FIG. 11 depicts one embodiment of a host computer system;

FIG. 12 depicts a further example of a computer system;

FIG. 13 depicts another example of a computer system comprising acomputer network;

FIG. 14 depicts one embodiment of various elements of a computer system;

FIG. 15A depicts one embodiment of the execution unit of the computersystem of FIG. 14;

FIG. 15B depicts one embodiment of the branch unit of the computersystem of FIG. 14;

FIG. 15C depicts one embodiment of the load/store unit of the computersystem of FIG. 14; and

FIG. 16 depicts one embodiment of an emulated host computer system.

DETAILED DESCRIPTION

In one aspect, a machine instruction is provided for generatingpseudorandom numbers. The instruction, referred to as a PerformPseudorandom Number Operation instruction, includes capabilities toinstantiate one or more seed values to be used to generate pseudorandomnumbers, reseed one or more seed values, and/or generate pseudorandomnumbers. As one example, the instruction uses a 512-bit secure hashalgorithm (SHA-512) specified by the National Institute of Standards andTechnology (NIST). It complies with the latest NIST recommendations forpseudorandom number generation. For performance reasons, however, theinstruction operates in a right-to-left manner, rather than aleft-to-right manner, as specified by NIST. In further embodiments, theinstruction is extendable to use alternate encoding algorithms (alsoreferred to as techniques).

One embodiment of a computing environment to incorporate and use one ormore aspects is described with reference to FIG. 1A. A computingenvironment 100 includes, for instance, a processor 102 (e.g., a centralprocessing unit), a memory 104 (e.g., main memory), and one or moreinput/output (I/O) devices and/or interfaces 106 coupled to one anothervia, for example, one or more buses 108 and/or other connections.

In one example, processor 102 is based on the z/Architecture offered byInternational Business Machines Corporation, and is part of a server,such as the System z server, which is also offered by InternationalBusiness Machines Corporation and implements the z/Architecture. Oneembodiment of the z/Architecture is described in an IBM® publicationentitled, “z/Architecture Principles of Operation,” IBM® Publication No.SA22-7832-09, Tenth Edition, September, 2012, which is herebyincorporated herein by reference in its entirety. In one example, theprocessor executes an operating system, such as z/OS, also offered byInternational Business Machines Corporation. IBM®, Z/ARCHITECTURE® andZ/OS® are registered trademarks of International Business MachinesCorporation, Armonk, N.Y., USA. Other names used herein may beregistered trademarks, trademarks, or product names of InternationalBusiness Machines Corporation or other companies.

In a further embodiment, processor 102 is based on the PowerArchitecture offered by International Business Machines Corporation. Oneembodiment of the Power Architecture is described in “Power ISA™ Version2.06 Revision B,” International Business Machines Corporation, Jul. 23,2010, which is hereby incorporated herein by reference in its entirety.POWER ARCHITECTURE® is a registered trademark of International BusinessMachines Corporation.

In yet a further embodiment, processor 102 is based on an Intelarchitecture offered by Intel Corporation. One embodiment of the Intelarchitecture is described in “Intel® 64 and IA-32 ArchitecturesDeveloper's Manual: Vol. 2B, Instructions Set Reference, A-L,” OrderNumber 253666-045US, January 2013, and “Intel® 64 and IA-32Architectures Developer's Manual: Vol. 2B, Instructions Set Reference,M-Z,” Order Number 253667-045US, January 2013, each of which is herebyincorporated herein by reference in its entirety. Intel® is a registeredtrademark of Intel Corporation, Santa Clara, Calif.

Processor 102 includes a plurality of functional components used toexecute instructions. As depicted in FIG. 1B, these functionalcomponents include, for instance, an instruction fetch component 120 tofetch instructions to be executed; an instruction decode unit 122 todecode the fetched instructions and to obtain operands of the decodedinstructions; an instruction execute component 124 to execute thedecoded instructions; a memory access component 126 to access memory forinstruction execution, if necessary; and a write back component 130 toprovide the results of the executed instructions. One or more of thesecomponents may, in accordance with an aspect, provide pseudorandomnumber seed and/or generate functionality by including at least aportion of or having access to a seed/generate component 136. Thisfunctionality is described in further detail below.

Processor 102 also includes, in one embodiment, one or more registers140 to be used by one or more of the functional components.

Another embodiment of a computing environment to incorporate and use oneor more aspects is described with reference to FIG. 2A. In this example,a computing environment 200 includes, for instance, a native centralprocessing unit (CPU) 202, a memory 204, and one or more input/outputdevices and/or interfaces 206 coupled to one another via, for example,one or more buses 208 and/or other connections. As examples, computingenvironment 200 may include a PowerPC processor, a pSeries server or anxSeries server offered by International Business Machines Corporation,Armonk, N.Y.; an HP Superdome with Intel Itanium II processors offeredby Hewlett Packard Co., Palo Alto, Calif.; and/or other machines basedon architectures offered by International Business Machines Corporation,Hewlett Packard, Intel, Oracle, or others.

Native central processing unit 202 includes one or more native registers210, such as one or more general purpose registers and/or one or morespecial purpose registers used during processing within the environment.These registers include information that represent the state of theenvironment at any particular point in time.

Moreover, native central processing unit 202 executes instructions andcode that are stored in memory 204. In one particular example, thecentral processing unit executes emulator code 212 stored in memory 204.This code enables the computing environment configured in onearchitecture to emulate another architecture. For instance, emulatorcode 212 allows machines based on architectures other than thez/Architecture, such as PowerPC processors, pSeries servers, xSeriesservers, HP Superdome servers or others, to emulate the z/Architectureand to execute software and instructions developed based on thez/Architecture.

Further details relating to emulator code 212 are described withreference to FIG. 2B. Guest instructions 250 stored in memory 204comprise software instructions (e.g., correlating to machineinstructions) that were developed to be executed in an architectureother than that of native CPU 202. For example, guest instructions 250may have been designed to execute on a z/Architecture processor 102, butinstead, are being emulated on native CPU 202, which may be, forexample, an Intel Itanium II processor. In one example, emulator code212 includes an instruction fetching routine 252 to obtain one or moreguest instructions 250 from memory 204, and to optionally provide localbuffering for the instructions obtained. It also includes an instructiontranslation routine 254 to determine the type of guest instruction thathas been obtained and to translate the guest instruction into one ormore corresponding native instructions 256. This translation includes,for instance, identifying the function to be performed by the guestinstruction and choosing the native instruction(s) to perform thatfunction.

Further, emulator 212 includes an emulation control routine 260 to causethe native instructions to be executed. Emulation control routine 260may cause native CPU 202 to execute a routine of native instructionsthat emulate one or more previously obtained guest instructions and, atthe conclusion of such execution, return control to the instructionfetch routine to emulate the obtaining of the next guest instruction ora group of guest instructions. Execution of the native instructions 256may include loading data into a register from memory 204; storing databack to memory from a register; or performing some type of arithmetic orlogic operation, as determined by the translation routine.

Each routine is, for instance, implemented in software, which is storedin memory and executed by native central processing unit 202. In otherexamples, one or more of the routines or operations are implemented infirmware, hardware, software or some combination thereof. The registersof the emulated processor may be emulated using registers 210 of thenative CPU or by using locations in memory 204. In embodiments, guestinstructions 250, native instructions 256 and emulator code 212 mayreside in the same memory or may be disbursed among different memorydevices.

As used herein, firmware includes, e.g., the microcode, millicode and/ormacrocode of the processor. It includes, for instance, thehardware-level instructions and/or data structures used inimplementation of higher level machine code. In one embodiment, itincludes, for instance, proprietary code that is typically delivered asmicrocode that includes trusted software or microcode specific to theunderlying hardware and controls operating system access to the systemhardware.

In one example, a guest instruction 250 that is obtained, translated andexecuted is the Perform Pseudorandom Number Operation instructiondescribed herein. The instruction, which is of one architecture (e.g.,the z/Architecture), is fetched from memory, translated and representedas a sequence of native instructions 256 of another architecture (e.g.,PowerPC, pSeries, xSeries, Intel, etc.). These native instructions arethen executed.

Details relating to the Perform Pseudorandom Number Operationinstruction, including explicit and implied fields of the instruction,as well as execution by a central processing unit (either in a native oremulated system), are described herein. The Perform Pseudorandom NumberOperation instruction includes a generate operation to generatepseudorandom numbers, as well as a seed operation to initiate or reseedone or more seed values used to generate the pseudorandom numbers. Theseed values are stored in a parameter block accessed by the instruction.

Referring initially to FIG. 3A, one embodiment of a Perform PseudorandomNumber Operation instruction is described. In one example, a PerformPseudorandom Number Operation instruction 300 includes an opcode field302 (e.g., bits 0-15) having an opcode (e.g., ^(|)B93C|) to indicate aperform pseudorandom number operation; a first register field 304 (e.g.,bits 24-27) used to designate at least one first register (R₁); and asecond register field 306 (e.g., bits 28-31) used to designate at leastone second register (R₂). Each of the fields 304-306, in one example, isseparate and independent from the opcode field. Further, in oneembodiment, they are separate and independent from one another; however,in other embodiments, more than one field may be combined.

In one example, selected bits (e.g., the first two bits) of the opcodedesignated by opcode field 302 specify the length of the instruction. Inthis particular example, the selected bits indicate that the length istwo halfwords. Further, the format of the instruction is aregister-and-register operation with an extended opcode field. With thisformat, the contents of the register designated by the R₁ field arecalled the first operand. The register containing the first operand issometimes referred to as the first operand location. Further, the R₂field designates the register containing the second operand, and R₂ maydesignate the same register as the R₁ field.

In addition to R₁ and R₂ encoded in the instruction, one implementationof the instruction uses one or more implied registers including, forinstance, general register 0 (GR0) and general register 1 (GR1). Each ofthe registers is further described below with reference to FIGS. 3B-3G.

Referring initially to FIG. 3B, one embodiment of a format of generalregister 0 (320) is described. In one example, general register 0includes a modifier (M) bit 322 (e.g., bit 56), and a function code (FC)field 324 (e.g., bits 57-63). The function code field includes afunction code specifying a function to be performed. In one example, theassigned function codes include: code 0 for a query function, which hasan assigned parameter block size of 16; and code 3 for an SHA-512-DRNG(Deterministic Random Number Generator) function, which has an assignedparameter block size of 240. Should bits 57-63 of general register 0designate an unassigned or uninstalled function code, a specificationexception is recognized.

The query function (function code 0) provides the means of indicatingthe availability of other functions, including, but not limited to,other random or pseudorandom number generator functions. The R₁ and R₂fields and the contents of general register 1 are ignored for the queryfunction.

In this embodiment, for functions other than the query function, bit 56is the modifier bit used to indicate a particular operation to beperformed. For instance, when the modifier bit is zero, a generateoperation is performed, and when the modifier bit is 1, a seed operationis performed. The modifier bit is ignored for the query function. Allother bits of general register 0 are ignored in one implementation. In afurther embodiment, if other functions are provided, they may or may notuse the modifier bit.

Use of the function code and modifier bit are further described withreference to FIGS. 3H and 3I. Initially, referring to FIG. 3H, a PerformPseudorandom Number Operation instruction is obtained, STEP 379, andexecuted. During execution, in one embodiment, a function code specifiedin general register 0 is obtained, STEP 380. A determination is made,based on the function code, as to the function to be performed, STEP382. As examples, the function may be a query function or a randomnumber generator function, such as the SHA-512-DRNG function, or othertypes of random number generator functions, or other functions.

Thereafter, a determination is made as to whether the function specifiedby the function code uses the modifier indicator, INQUIRY 384. If themodifier indicator is not used, then processing proceeds with performingthe designated function, STEP 386. Otherwise, the modifier indicator isobtained, STEP 388, and processing proceeds based on the modifierindicator, STEP 390.

One embodiment of use of the modifier indicator is further describedwith reference to FIG. 3I. Initially, a determination is made as to thevalue of the modifier indicator, INQUIRY 392. In one particular examplein which the function code indicates the SHA-512-DRNG function, adetermination is made as to whether the value of the modifier indicatoris either a 0 or a 1.

If the value of the modifier bit is 0, then the generate operation ofthe SHA-512-DRNG function is performed, STEP 394. This includes, forinstance, generating, for each block of memory of the first operand, ahash value using the 512 bit secure hash technique and one or more seedvalues in the parameter block; and storing at least a portion of thegenerated hash value in the first operand.

Otherwise, if the value of the modifier bit is 1, then a seed operationis performed, STEP 396. This includes, for instance, obtaining seedmaterial, which is formed based on a value of a reseed counter and usinginformation included in the second operand of the instruction; using theseed material and the 512 bit secure hash technique to provide one ormore seed values; and storing the seed value(s) in the parameter block.

In other embodiments in which the function code represents other typesof random number generator functions, the same modifier bit values maybe used to determine whether a generate or seed operation is to beperformed for that random number generator function. Additionally, infurther embodiments, for other types of function codes specifying othertypes of functions, the value of the modifier indicator may specifydifferent operations than described herein. Many variations arepossible.

Continuing with a description of the instruction registers, referring toFIG. 3C, one embodiment of a format of general register 1 (330) isdescribed. In one example, for functions other than the query function,general register 1 contains a logical address 332 of the leftmost byteof the parameter block in storage to be accessed and used by theinstruction. The length and position of the parameter block addresswithin general register 1 depends on the addressing mode. In the 24-bitaddressing mode, the contents of bit positions 40-63 of general register1 constitute the address, and the contents of bit positions 0-38 areignored. In the 31-bit addressing mode, the contents of bit positions33-63 of general register 1 constitute the address, and the contents ofbit positions 0-32 are ignored. In the 64-bit addressing mode, thecontents of bit positions 0-63 of general register 1 constitute theaddress. In the access-register mode, access register 1 specifies theaddress space containing the parameter block.

FIG. 3D depicts one example of the contents of R₁ (340) designated by R₁field 304 (FIG. 3A). In particular, for the generate operation, the R₁field designates an even-odd pair of general registers and is todesignate an even-numbered register other than general register 0;otherwise, a specification exception is recognized. The contents ofgeneral register R₁ specify a location in memory of the first operand.In particular, the contents of R₁ specify an address 342 of the leftmostbyte of the first operand. The length 352 (FIG. 3E) of the first operandis specified in general register R₁+1 (350). The R₂ field is ignored bythe generate operation.

For a seed operation, the R₂ field 306 (FIG. 3A) designates an even-oddpair of general registers and is to designate an even-numbered registerother than general register 0; otherwise, a specification exception isrecognized. The contents of general register R₂ (360, FIG. 3F) specify alocation in memory of the second operand. In particular, the contents ofR₂ specify an address 362 of the leftmost byte of the second operand.The length 372 (FIG. 3G) of the second operand is specified in generalregister R₂+1 (370). The R₁ field is ignored by a seed operation.

Regardless of whether a generate or seed operation is specified, thecontents of the even-numbered general register designating the storageoperand (R₁ or R₂, respectively) are subject to the addressing mode. Inthe 24-bit addressing mode, the contents of bit positions 40-63 of theregister constitute the address of the storage operand, and the contentsof bit positions 0-39 are ignored. In the 31-bit addressing mode, thecontents of bit positions 33-63 of the register constitute the addressof the storage operand, and the contents of bit positions 0-32 areignored. In the 64-bit addressing mode, the contents of bit positions0-63 of the register constitute the address of the storage operand. Inthe access-register mode, the respective access register (R₁ or R₂)specifies the address space containing the storage operand.

Regardless of whether a generate or seed operation is specified, in boththe 24-bit and the 31-bit addressing modes, the contents of bitpositions 32-63 of the odd-numbered general register (R₁+1 or R₂+1,respectively) form a 32-bit unsigned binary integer which specifies thenumber of bytes in the storage operand. In the 64-bit addressing mode,the contents of bit positions 0-63 of the register form a 64-bitunsigned binary integer which specifies the number of bytes in thestorage operand.

For a generate operation, the first operand length is updated in generalregister R₁+1 at the completion of the instruction. In both the 24-bitand the 31-bit addressing modes, the updated value replaces the contentsof bit positions 32-63 of general register R₁+1; the contents of bitpositions 0-31 of general register R₁+1 remain unchanged. In the 64-bitaddressing mode, the updated value replaces the contents of generalregister R₁+1.

When the parameter block overlaps any portion of the storage operand,the results are unpredictable.

When the storage operand length is zero, access exceptions for thestorage operand location are not recognized. However, the parameterblock is accessed even when the storage operand length is zero. For agenerate operation, when the storage operand length is zero, generalregister R₁+1 is not changed, and condition code 0 is set.

As observed by other CPUs and the I/O subsystem, references to theparameter block and storage operand may be multiple access references,accesses to these locations are not necessarily block concurrent, andthe sequence of these accesses or references is undefined.

For a generate operation, when a PER (Program EventRecording—implemented on, for instance, processors based on thez/Architecture) storage alteration event is recognized, fewer than 4Kadditional bytes are stored into the first operand location before theevent is reported. When a PER storage alteration event is recognizedboth for the first operand location and for the portion of the parameterblock that is stored, it is unpredictable which of these two locationsis indicated in the PER access identification (PAID) and PER ASCE ID(Program Event Recording address space control element identification(AI)). Similarly, when a PER zero-address-detection event is recognizedfor both for the first operand location and for the parameter block, itis unpredictable which of these two locations is identified in the PAIDand AI.

For a generate operation, access exceptions may be reported for a largerportion of the first operand than is processed in a single execution ofthe instruction. However, access exceptions are not recognized forlocations that do not encompass the first operand nor for locations morethan 4K bytes from the current location being processed.

For a generate operation, when the operation ends due to normalcompletion, condition code 0 is set and the resulting value in generalregister R₁+1 is zero. When the operation ends due to partialcompletion, condition code 3 is set and the resulting value in generalregister R₁+1 is nonzero.

In one implementation, when the function code of the PerformPseudorandom Number Operation instruction is 0 indicating a queryfunction, a 128-bit status word 402 (FIG. 4A) is stored in a parameterblock 400 associated with the instruction. Bits 0-127 of this fieldcorrespond to function codes 0-127, respectively, of the PerformPseudorandom Number Operation instruction. When a bit is one, thecorresponding function is installed; otherwise, the function is notinstalled. For instance, if the SHA-512 DRNG function is installed, bit3, corresponding to function code 3, is set to one.

Condition code 0 is set when execution of the Query function completes;condition code 3 is not applicable to this function.

In one implementation, when the function code of the PerformPseudorandom Number Operation instruction is 3, a deterministic randomnumber generator (DRNG) function is performed. Depending on the modifierbit, bit 56 of general register 0, the DRNG function performs either adeterministic pseudorandom number generate operation or a deterministicpseudorandom number seed operation, each using the 512-bit secure hashalgorithm (SHA-512).

Deterministic pseudorandom number generation, also known asdeterministic random bit generation, is defined in, for instance,Recommendation for Random Number Generation Using Deterministic RandomBit Generators , National Institute of Standards and Technology (NIST),NIST Special Publication 800-90A, January 2012, which is herebyincorporated herein by reference in its entirety. Further, a descriptionof the secure hash algorithm is found in, for instance, Secure HashStandard (SHS), Federal Information Processing Standards Publication,FIPS PUB 180-4, National Institute of Standards and Technology,Gaithersburg, Md., March 2012, which is hereby incorporated herein byreference in its entirety.

One embodiment of a parameter block used for the DRNG function isdepicted in FIG. 4B. Parameter block 420 represents the internal stateof a deterministic random number generator, and includes, for instance:

-   -   Reserved: Bytes 0-3, 16, and 128 of the parameter block are        reserved.    -   Reseed Counter 422: Bytes 4-7 of the parameter block contain a        32-bit unsigned binary integer indicating the number of times        that the instruction has completed with condition code 0 since        the parameter block was last instantiated or reseeded.    -   When the reseed counter contains zero, the following applies:        -   Execution of the seed operation causes the parameter block            to be instantiated with initial values, including setting            the reseed counter to a value of one.        -   Execution of the generate operation results in a            specification exception being recognized.    -   When the reseed counter contains a nonzero value, the parameter        block is considered to be instantiated, and the following        applies:        -   Execution of the seed operation causes the parameter block            to be reseeded, including resetting the reseed counter to a            value of one.        -   Execution of a generate operation that results in condition            code 0 causes the reseed counter to be incremented by one;            any carry out of bit position 0 of the reseed counter field            is ignored.    -   Stream Bytes 424: Bytes 8-15 of the parameter block contain a        64-bit unsigned binary integer. The stream bytes field is set to        zero by the execution of the seed operation when instantiating        the parameter block (that is, when the reseed counter is zero);        the field is not changed by the execution of the seed operation        when the parameter block is already instantiated.    -   Partial or full completion of a generate operation causes the        contents of the stream bytes field to be incremented by the        number of bytes stored into the first operand; any carry out of        bit position 0 of the stream bytes field is ignored.    -   Value (V) 426: Bytes 17-127 of the parameter block contain, for        instance, an 888-bit value indicating the internal state of the        random number generator represented by the parameter block. V is        initialized by the execution of the seed operation when        instantiating the parameter block. V is updated by either (a)        the execution of the seed operation when the reseed counter is        nonzero, or (b) the execution of the generate operation that        ends in condition code 0.    -   Constant (C) 428: Bytes 129-239 of the parameter block contain,        for instance, an 888-bit value indicating the internal state of        the random number generator represented by the block. C is        initialized by the execution of the seed operation, and        inspected by the generate operation.

The same parameter block format is used by both the generate operationand the seed operation (including instantiation and reseeding). Aparameter block containing all zeros is considered to be notinstantiated. The program should zero the parameter block prior toissuing the seed operation to instantiate the parameter block, andsubsequently, the program should not alter the contents of the parameterblock except to zero it; otherwise, unpredictable results may beproduced by the instruction.

Further details regarding the seed operation and the generate operationof the DRNG function (also referred to herein as the SHA-512-DRNGfunction) are described below.

Seed Operation

The SHA-512-DRNG seed operation instantiates or reseeds a deterministicpseudorandom number generation parameter block using the 512-bit securehash algorithm. In one embodiment, the operation is performed by acentral processing unit; however, in other embodiments, it is performedby other components or co-processors.

Depending on whether the reseed counter in bytes 4-7 of the parameterblock is zero or nonzero, an instantiation or reseeding operation isperformed, respectively. Further details of instantiation and reseedingare described below with reference to the figures. In the figures, theindicated symbols/abbreviations have the following meaning: <#>: lengthof field in bytes; R₂+1: the length of operand 2 in storage in the rangeof 0-512 bytes; #bits: 32-bit count of bits to be produced by theSHA-512 algorithm—888 bits (378 hex); ct: 8-bit counter (e.g., m used bythe hash derivation function); z: 8-bit field of zeros.

-   -   For the instantiation operation, as depicted in FIG. 5A, the        second operand in storage 500 a includes one or more of entropy        input, nonce, and an optional personalization string, each of        which is described below. This information is used to form seed        material 502 a.    -   As an example, entropy input is an input bitstring that provides        an assessed minimum amount of unpredictability for a        Deterministic Random Bit Generator (DRBG) mechanism. A DRBG        mechanism is the portion of a random bit generator (RBG) that        includes the functions to instantiate and uninstantiate the RBG,        generate pseudorandom bits, optionally reseed the RBG, and test        the health of the DRBG mechanism.    -   A Random Bit Generator (RBG) is a device, algorithm, technique        or mechanism that outputs a sequence of binary bits that appear        to be statistically independent and unbiased. One example of an        RBG is a DRBG. A DRBG is, for instance, an RBG that includes a        DRBG mechanism and (at least initially) has access to a source        of entropy input. The DRBG produces a sequence of bits from a        secret initial value called a seed, along with other possible        inputs.    -   A seed is a string of bits that is used as input to a DRBG        mechanism. The seed determines a portion of the internal state        of the DRBG, and its entropy is to be sufficient to support the        security strength of the DRBG. Entropy is a measure of the        disorder, randomness or variability in a closed system.        Min-entropy is the measure used in one implementation    -   The min-entropy (in bits) of a random variable X is the largest        value m having the property that each observation of X provides        at least m bits of information (i.e., the min-entropy of X is        the greatest lower bound for the information content of        potential observations of X). The min-entropy of a random        variable is a lower bound on its entropy. The precise        formulation for min-entropy is −(log₂ max p_(i)) for a discrete        distribution having probabilities p₁, . . . , p_(n). Min-entropy        is often used as a worst case measure of the unpredictability of        a random variable.    -   Nonce is a time-varying value that has at most a negligible        chance of repeating, e.g., a random value that is generated anew        for each use, a timestamp, a sequence number, or some        combination of these.    -   Personalization string is an optional string of bits that is        combined with a secret entropy input and (possibly) a nonce to        produce a seed.    -   For the reseed operation (a reseed acquires additional bits that        affect the internal state of the DRBG mechanism), the second        operand in storage 500 b (FIG. 5B) includes entropy input and        optional additional input, used to form the seed material 502 b.        The optional additional input may be any desired information        that adds further randomness, such as a time value or other        arbitrary values, as examples.

When performing an instantiation operation, seed material is formedusing only the second operand, as depicted in FIG. 5A. For instance,input values of the second operand are concatenated to form the seedmaterial. However, when performing a reseed operation, seed material isformed, as shown in FIG. 5B, from a concatenation of, for instance, thevalue 01 hex (504), the contents of V field 506 of the parameter block,and the contents of second operand 500 b.

For either the instantiation or reseed operation, one or more seedvalues are initialized/updated. One such seed value is V_(new), which isformed as described with reference to FIG. 6. In one embodiment, a onebyte counter 600 a, a four-byte value of 888 (602 a), seed material 604a (formed as described above), and padding 606 a are concatenated andused as input to a SHA-512 algorithm 608 a, along with an initial hashvalue (IHV) (also referred to as an initial chaining value (ICV)) 610 a.In one embodiment, the padding is a value of 80 hex, concatenated with0-127 bytes of zeros, concatenated with a 16-byte binary integerdesignating the length in bits of the input to the SHA-512 algorithm notincluding the padding (that is, the length of the one-byte counter,four-byte value of 888, and the seed material). The initial hash valueis, for instance, a 64 byte value, and examples of such values aredescribed further below.

The SHA-512 algorithm is invoked twice to form two 64-bit hashed results612 a, 612 b; the one-byte counter 600 a contains the value 1 for thefirst invocation of the SHA-512 algorithm, and it contains the value 2(600 b) for the second invocation. The second invocation also uses afour byte value of 888 (602 b), seed material 604 b, and padding 606 bas input to SHA-512 algorithm 608 b, along with IHV 610 b to form 64-bithashed result 612 b. In this example, 602 b is the same value as 602 a;604 b is the same as 604 a; 606 b is the same as 606 a; and 610 b is thesame as 610 a. However, in other embodiments, for instance, for othertechniques, the values may be different from one another.

The two 64-byte hashed results 612 a, 612 b are concatenated together,and, in this example, the leftmost 111 bytes of the 128-byteconcatenation form the new Value field (V_(new)) 614 in the parameterblock.

Similar to the formation of the V_(new) field, a new constant field(C_(new)) is formed during both the instantiation or reseedingoperation. C_(new) is another seed value stored in the parameter block.As shown in FIG. 7, a one byte counter 700 a, a four-byte value of 888(702 a), a one byte value of zero 704 a, V_(new) field 706 a, andpadding 708 a are concatenated and used as input to an SHA-512 algorithm710 a, along with an IHV 711 a. The padding is, for instance, a value of80 hex, concatenated with 122 bytes of zeros, concatenated with a16-byte binary integer designating the length in bits of the input tothe SHA-512 algorithm not including the padding (that is, the length ofthe one-byte counter, four-byte value of 888, one-byte value of zero,and the V_(new) field). IHV 711 a is the same value, in one embodiment,as IHV 610 a or IHV 610 b.

The SHA-512 algorithm is invoked twice to form two 64-bit hashed results712 a, 712 b; the one-byte counter 700 a contains the value 1 for thefirst invocation of the SHA-512 algorithm, and it contains the value 2(700 b) for the second invocation. The second invocation also uses afour byte value of 888 (702 b), a one byte value of zero (704 b),V_(new) field 706 b, and padding 708 b as input to SHA-512 algorithm 710b, along with IHV 711 b. In this example, 702 b is the same as 702 a;704 b is the same as 704 a; 706 b is the same as 706 a; 708 b is thesame as 708 a; and 711 b is the same as 711 a. However, in otherembodiments, for instance, for other techniques, they may be differentfrom one another.

The two 64-byte hashed results 712 a, 712 b are concatenated together,and, in this example, the leftmost 111 bytes of the 128-byteconcatenation form the new constant field (C_(new)) 714.

For either the instantiate or reseed operation, the reseed counter field720 in the parameter block is set to the value of one. For theinstantiate operation only, the stream bytes field 722 in the parameterblock is set zeros; the stream bytes field remains unchanged by a reseedoperation.

Condition code 0 is set when execution of the SHA-512-DRNG seedoperation completes; condition code 3 is not applicable to the seedoperation.

Generate Operation

The SHA-512-DRNG generate operation generates pseudorandom numbers usingthe parameter block instantiated or reseeded, as described above, aswell as the 512-bit secure hash algorithm. In one embodiment, theoperation is performed by a central processing unit; however, in otherembodiments, it is performed by other components or co-processors.

When the first operand length in general register R₁+1 is nonzero, thefirst operand is stored in right-to-left order in units of 64-byteblocks, except that the rightmost block may contain fewer than 64 bytes.The number of blocks to be stored, including any partial rightmostblock, is determined by rounding the first operand length in generalregister R₁+1 up to a multiple of 64 and dividing the value by 64. Theblocks of the first operand are numbered from left to right as 0 to n−1,where n−1 represents the rightmost block.

The following procedure is performed, in one implementation, for eachblock of the first operand location, beginning with the rightmost (n−1)block and proceeding to the left, as described with reference to FIGS.8A-8B. In FIG. 8B (and FIG. 9), <#> refers to the length of the field inbytes.

Referring initially to FIG. 8A, for a block of the first operandlocation, a hash value is generated, STEP 801. One embodiment ofgenerating the hash value is described with reference to FIG. 8B.

-   -   1. Referring to FIG. 8B, the value (V) 802 from parameter block        800 is added 804 to the block number 806 being processed, with        any overflow from the addition ignored.    -   2. The 111-byte sum of this addition 808, concatenated with 17        bytes of padding 810, are used as input to the SHA-512 algorithm        812, along with IHV 811, resulting in a 64-byte hashed value        814. The 17-byte padding provided to the SHA-512 algorithm is,        for instance, a value of 80 hex followed by a 16-byte binary        integer value of 888 (the length of V in bits). IHV 811 is the        same as one of IHV 610 a, 610 b, 71 la or 711 b; or, in another        embodiment, for instance, for other techniques, it may have a        different value.    -   3. Returning to FIG. 8A, subsequent to creating the hashed        value, if the first operand length in general register R₁+1 is a        multiple of 64, INQUIRY 803, then the resulting 64-byte hashed        value is stored in the respective block of the first operand        location, STEP 805, and the length in general register R₁+1 is        decremented by 64, STEP 807.        -   If the first operand length is not a multiple of 64, INQUIRY            803, then the leftmost m bytes of the resulting 64-byte            hashed value is stored in the rightmost partial block of the            first operand, where m represents the remainder of the first            operand length divided by 64, STEP 809. In this case, the            length in general register R₁+1 is decremented by m, STEP            807.    -   4. Regardless of whether a full or partial block is stored,        stream bytes field 816 (FIG. 8B) in bytes 8-15 of parameter        block 800 is incremented by the number of bytes stored into the        first operand location, STEP 811 (FIG. 8A).

The above process is repeated 820 a-820 n until either the first operandlength in general register R₁+1 is zero (called normal completion) or aCPU-determined number of blocks has been processed (called partialcompletion), INQUIRY 813 (FIG. 8A). The CPU-determined number of blocksdepends on the model, and may be a different number each time theinstruction is executed. The CPU-determined number of blocks is usuallynonzero. In certain unusual situations, this number may be zero, andcondition code 3 may be set with no progress. However, the CPU protectsagainst endless reoccurrence of this no-progress case.

Based on performing the generate operation, the first operand includes apseudorandom number.

When the first operand length in general register R₁+1 is initiallyzero, normal completion occurs without storing into the first operandlocation; however, the parameter block is updated, as described withreference to FIG. 9. Further, when the pseudorandom number generationprocess ends due to normal completion, the parameter block is updated asdescribed with reference to FIG. 9.

Referring to FIG. 9, in one embodiment, the parameter block is updated,as follows:

-   -   1. A one byte value of 03 hex (902), a 111-byte value (V) 904        from parameter block 900, and 144 bytes of padding 906 are        concatenated and used as input to the SHA-512 algorithm 908,        along with IHV 909, resulting in a 64-byte hashed value 910. The        padding is, for instance, a value of 80 hex, concatenated with        127 bytes of zeros, concatenated with a 16-byte binary integer        designating the length in bits of the input to the SHA-512        algorithm not including the padding (that is, the length of the        one-byte value of 03 hex and the V field). IHV 909 is, in one        embodiment, equal to one of IHV 610 a, 610 b, 711 a, 711 b or        811; or, in another embodiment, for instance, for other        techniques, it may be a different value.    -   2. The values of the 4-byte reseed counter field 912 and the        111-byte value (V) 904 and constant (C) 914 fields in parameter        block 900, and the 64-byte hashed value (from the above        computation) 910 are added 920. Any overflow from the addition        is ignored, and the resulting 111-byte sum 922 replaces the        Value field (V_(new)) 904 in parameter block 900.    -   3. The 4-byte reseed counter field 912 in parameter block 900 is        incremented by one.    -   4. Condition code 0 is set.

When the pseudorandom number generation process ends due to partialcompletion, the first operand length in general register R₁+1 contains anonzero multiple of 64, the reseed counter and value (V) fields in theparameter block are not updated, and condition code 3 is set.

In one particular embodiment, a specification exception is recognizedand no other action is taken if any of the following conditions exist:

-   -   1. Bits 57-63 of general register 0 specify an unassigned or        uninstalled function code.    -   2. The following special conditions apply to the generate        operation:        -   The R₁ field designates an odd-numbered register or general            register 0.        -   The reseed counter in the parameter block is zero.    -   3. The following special conditions apply to the seed operation:        -   The R₂ fields designates an odd-numbered register or general            register 0 (seed operation only.)        -   The length in general register R₂+1 is greater than 512.

Condition Code

0 Normal completion

1—

2—

3 Partial completion (generate operation only)

Program Exceptions:

-   -   Access (store, operand 1, generate operation; fetch, operand 2,        seed operation; fetch and store, parameter block)    -   Operation (if message-security-assist extension 5 (of the        z/Architecture) is not installed)    -   Specification    -   Transaction constraint

One embodiment of further details of the SHA-512 algorithm is nowdescribed.

SHA-512

SHA-512 may be used to hash a message, M, having a length of l bits,where 0≦l<2¹²⁸. The algorithm uses 1) a message schedule of eighty64-bit words, 2) eight working variables of 64 bits each, and 3) a hashvalue of eight 64-bit words. The final result of SHA-512 is a 512-bitmessage digest.

The words of the message schedule are labeled W₀, W₁, . . . , W₇₉. Theeight working variables are labeled a, b, c, d, e, f, g, and h. Thewords of the hash value are labeled H₀ ^((i)), H₁ ^((i)), . . . , H₇^((i)), which will hold the initial hash value, H^((o))), replaced byeach successive intermediate hash value (after each message block isprocessed), H^((i)), and ending with the final hash value, H^((N)).SHA-512 also uses two temporary words, T₁ and T₂.

The SHA-512 algorithm may use one or more of the following parameters:

-   -   a, b, c, . . . , h Working variables that are the w-bit words        used in the computation of the hash values, H^((i)).    -   H^((i)) The i^(th) hash value. H⁽⁰⁾ is the initial hash value;        H^((N)) is the final hash value and is used to determine the        message digest.    -   H_(j) ^((i)) The j^(th) word of the i^(th) hash value, where H₀        ^((i)) is the leftmost word of hash value i.    -   K_(t) Constant value to be used for the iteration t of the hash        computation.        -   SHA-512 uses a sequence of eighty constant 64-bit words, K₀            ^({512)}, K₁ ^({512}), . . . , K₇₉ ^({512}). These words            represent the first sixty-four bits of the fractional parts            of the cube roots of the first eighty prime numbers. In hex,            these constant words are (from left to right)

428a2f98d728ae22 7137449123ef65cd b5c0fbcfec4d3b2f e9b5dba58189dbbc3956c25bf348b538 59f111f1b605d019 923f82a4af194f9b ab1c5ed5da6d8118d807aa98a3030242 12835b0145706fbe 243185be4ee4b28c 550c7dc3d5ffb4e272be5d74f27b896f 80deb1fe3b1696b1 9bdc06a725c71235 c19bf174cf692694e49b69c19ef14ad2 efbe4786384f25e3 0fc19dc68b8cd5b5 240ca1cc77ac9c652de92c6f592b0275 4a7484aa6ea6e483 5cb0a9dcbd41fbd4 76f988da831153b5983e5152ee66dfab a831c66d2db43210 b00327c898fb213f bf597fc7beef0ee4c6e00bf33da88fc2 d5a79147930aa725 06ca6351e003826f 142929670a0e6e7027b70a8546d22ffc 2e1b21385c26c926 4d2c6dfc5ac42aed 53380d139d95b3df650a73548baf63de 766a0abb3c77b2a8 81c2c92e47edaee6 92722c851482353ba2bfe8a14cf10364 a81a664bbc423001 c24b8b70d0f89791 c76c51a30654be30d192e819d6ef5218 d69906245565a910 f40e35855771202a 106aa07032bbd1b819a4c116b8d2d0c8 1e376c085141ab53 2748774cdf8eeb99 34b0bcb5e19b48a8391c0cb3c5c95a63 4ed8aa4ae3418acb 5b9cca4f7763e373 682e6ff3d6b2b8a3748f82ee5defb2fc 78a5636f43172f60 84c87814a1f0ab72 8cc702081a6439ec90befffa23631e28 a4506cebde82bde9 bef9a3f7b2c67915 c67178f2e372532bca273eceea26619c d186b8c721c0c207 eada7dd6cde0eb1e f57d4f7fee6ed17806f067aa72176fba 0a637dc5a2c898a6 113f9804bef90dae 1b710b35131c471b28db77f523047d84 32caab7b40c72493 3c9ebe0a15c9bebc 431d67c49c100d4c4cc5d4becb3e42b6 597f299cfc657e2a 5fcb6fab3ad6faec 6c44198c4a475817

-   -   k Number of zeros appended to a message during the padding step.    -   l Length of the message, M, in bits.    -   m Number of bits in a message block, M^((i)). For SHA-512, each        message block has 1024 bits, which are represented as a sequence        of sixteen 64-bit words.    -   M Message to be hashed.    -   M^((i)) Message block i, with a size of m bits.    -   M_(j) ^((i)) The j^(th) word of the i^(th) message block, where        M₀ ^((i)) is the leftmost word of message block i.    -   n Number of bits to be rotated or shifted when a word is        operated upon.    -   N Number of blocks in the padded message.    -   T Temporary w-bit word used in the hash computation.    -   w Number of bits in a word.    -   W_(t) The t^(th) w-bit word of the message schedule.

Further, one or more of the following symbols is used in the secure hashalgorithm specification; each operates on w-bit words:

-   -   Bitwise AND operation.    -   Bitwise OR (“inclusive-OR”) operation.    -   ⊕ Bitwise XOR (“exclusive-OR”) operation.    -   Bitwise complement operation.    -   + Addition modulo 2^(w).    -   << Left-shift operation, where x<<n is obtained by discarding        the leftmost n bits of the word x and then padding the result        with n zeros on the right.    -   >> Right-shift operation, where x>>n is obtained by discarding        the rightmost n bits of the word x and then padding the result        with n zeros on the left.

Yet further, one or more of the following operations is used in thesecure hash algorithm specification:

-   -   ROTL^(n)(x) The rotate left (circular left shift) operation,        where x is a w-bit word and n is an integer with 0≦n<w, is        defined by ROTL^(n)(x)=(x<<n)        (x>>w−n).    -   ROTR^(n)(x) The rotate right (circular right shift) operation,        where x is a w-bit word and n is an integer with 0≦n<w, is        defined by ROTR^(n)(x)=(x>>n)        (x<<w−n).    -   SHR^(n)(x) The right shift operation, where x is a w-bit word        and n is an integer with 0≦n<w, is defined by SHR^(n)(x)=x>>n

Moreover, the following operations are applied to w-bit words in the512-bit secure hash algorithm. SHA-512 operates on 64-bit words (w=64).

-   -   1. Bitwise logical word operations:        ,        , ⊕, and        .    -   2. Additional modulo 2^(w).        -   The operation x+y is defined as follows. The words x and y            represent integer X and Y, where 0≦X<2^(w) and 0≦Y<2^(w).            For positive integers U modV, let U and V be the remainder            upon dividing U by V. Compute            Z=(X+Y)mod 2^(w).        -   Then 0≦Z<2^(w). Convert the integer to Z to a word, z, and            define z=x+y.    -   3. The right shift operation SHR^(n)(x), where x is a w-bit word        and n is an integer with 0≦n<w, is defined by        SHR ^(n)(x)=x>>n.    -   4. The rotate right (circular right shift) operation        ROTR^(n)(x), where x is a w-bit word and n is an integer with        0≦n<w, is defined by        ROTR ^(n)(x)=(x>>n)        (x<<w−n).        -   Thus, ROTR^(n)(x) is equivalent to a circular shift            (rotation) of x by n positions to the right.    -   5. Note the following equivalence relationships, where w is        fixed in each relationship:        ROTL ^(n)(x)≈ROTR ^(w-n)(x)        ROTR ^(n)(x)≈ROTL ^(w-n)(x)

Additionally, SHA-512 uses one or more of six logical functions, whereeach function operates on 64-bit words, which are represented as x, y,and z. The result of each function is a new 64-bit word.

-   -   Ch(x,y,z)=(x        y)⊕(        x        z)    -   Maj(x,y,z)=(x        y)⊕(x        z)⊕(y        z)    -   Σ₀ ^({512})(x)=ROTR²⁸(x)⊕ROTR³⁴(x)⊕ROTR³⁹(x)    -   Σ₁ ^({512})(x)=ROTR¹⁴(x)⊕ROTR¹⁸(x)⊕ROTR⁴¹(x)    -   σ₀ ^({512})(x)=ROTR¹(x)⊕ROTR⁸(x)⊕SHR⁷(x)    -   σ₁ ^({512})(x)=ROTR¹⁹(x)⊕ROTR⁶¹(x)⊕SHR⁶(x)

SHA-512 is described in two stages: Preprocessing and Hash Computation.

SHA-512 Preprocessing

Preprocessing involves padding a message, parsing the padded messageinto m-bit blocks, and setting initialization values to be used in thehash computation. Initialization, padding and parsing are describedbelow.

Initialization

Set the initial hash value, H⁽⁰⁾, as described below.

For SHA-512, the initial hash value, H⁽⁰⁾, shall include the followingeight 64-bit words, in hex:

-   -   H₀ ⁽⁰⁾=6a09e667f3bcc908    -   H₁ ⁽⁰⁾=bb67ae8584caa73b    -   H₂ ⁽⁰⁾=3c6ef372fe94f82b    -   H₃ ⁽⁰⁾=a54ff53a5f1d36f1    -   H₄ ⁽⁰⁾=510e527fade682d1    -   H₅ ⁽⁰⁾=9b05688c2b3e6c1f    -   H₆ ⁽⁰⁾=1f83d9abfb41bd6b    -   H₇ ⁽⁰⁾=5be0cd19137e2179

The words are obtained by taking the first sixty-four bits of thefractional parts of the square roots of the first eight prime numbers.

Padding the Message

The purpose of this padding is to ensure that the padded message is amultiple of 512 or 1024 bits, depending on the algorithm. Padding can beinserted before hash computation begins on a message, or at any othertime during the hash computation prior to processing the block(s) thatwill contain the padding.

Suppose the length of the message M, in bits, is l bits. Append the bit“1” to the end of the message, followed by k zero bits, where k is thesmallest non-negative solution to the equation l+1+k=896 mod 1024. Thenappend the 128-bit block that is equal to the number l expressed using abinary representation. For example, the (8-bit ASCII) message “abc” haslength 8×3=24, so the message is padded with a one bit, then896−(24+1)=871 zero bits, and then the message length, to become the1024-bit padded message

$\underset{\underset{``a"}{︸}}{01100001}\mspace{14mu}\underset{\underset{``b"}{︸}}{01100010}\mspace{14mu}\underset{\underset{``c"}{︸}}{01100011}\mspace{14mu} 1\mspace{14mu}\overset{\overset{871}{︷}}{00\mspace{14mu}\ldots\mspace{14mu} 00}\mspace{14mu}\overset{\overset{128}{︷}}{00\mspace{14mu}\ldots\mspace{14mu} 0\underset{\underset{l = 24}{︸}}{11000}}$

The length of the padded message is now a multiple of 1024 bits.

Parsing the Message

The message and its padding are parsed into N m-bit blocks.

For SHA-512, the message and its padding are parsed into N 1024-bitblocks, M⁽¹⁾, . . . , M^((N)). Since the 1024 bits of the input blockmay be expressed as sixteen 64-bit words, the first 64 bits of messageblock i are denoted M₀ ^((i)), the next 64 bits are M₁ ^((i)), and so onup to M₁₅ ^((i)).

SHA-512 Hash Computation

The hash computation generates a message schedule from the paddedmessage and uses that schedule along with functions, constants, and wordoperations to iteratively generate a series of hash values. The finalhash value generated by the hash computation is used to determine themessage digest.

The SHA-512 hash computation uses functions and constants, as describedherein, and addition (+) is performed modulo 2⁶⁴.

Each message block, M⁽¹⁾, M⁽²⁾, . . . , M^((N)), is processed in order,using the following steps:

  For i=1 to N:  {   1. Prepare the message schedule, {W_(t)}:   $W_{t} = \left\{ \begin{matrix}M_{t}^{(i)} & {0 \leq t \leq 15} \\{{\sigma_{1}^{\{ 512\}}\left( W_{t - 2} \right)} + W_{t - 7} + {\sigma_{0}^{\{ 512\}}\left( W_{t - 15} \right)} + W_{t - 16}} & {16 \leq t \leq 79}\end{matrix} \right.$   2. Initialize the eight working variables, a, b,c, d, e, f, g, and h,    with the (i−1)^(st) hash value:     a = H₀^((i−1))     b = H₁ ^((i−1))     c = H₂ ^((i−1))     d = H₃ ^((i−1))    e = H₄ ^((i−1))     f = H₅ ^((i−1))     g = H₆ ^((i−1))     h = H₇^((i−1))   3. For t=0 to 79:    {    T₁ = h + Σ₁ ^({512})(e) + Ch(e, f,g) + K_(t) ^({512}) + W_(t)    T₂ = Σ₀ ^({512})(a) + Maj(a, b, c)    h =g    g = f    f = e    e = d + T₁    d = c    c = b    b = a    a = T₁ +T₂    }   4. Computer the i^(th) intermediate hash value H^((i)):     H₀^((i)) = a + H₀ ^((i−1))     H₁ ^((i)) = b + H₁ ^((i−1))     H₂ ^((i)) =c + H₂ ^((i−1))     H₃ ^((i)) = d + H₃ ^((i−1))     H₄ ^((i)) = e + H₄^((i−1))     H₅ ^((i)) = f + H₅ ^((i−1))     H₆ ^((i)) = g + H₆ ^((i−1))    H₇ ^((i)) = h + H₇ ^((i−1)) }

After repeating steps one through four a total of N times (i.e., afterprocessing M^((N))), the resulting 512-bit message digest of themessage, M, isH ₀ ^((N)) ∥H ₁ ^((N)) ∥H ₂ ^((N)) ∥H ₃ ^((N)) ∥H ₄ ^((N)) ∥H ₅ ^((N))∥H ₆ ^((N)) ∥H ₇ ^((N))where ∥ is concatenation.

Described above is one example of a CPU instruction to initially seed orreseed a pseudorandom number generator and/or to perform a generateoperation to produce pseudorandom numbers. This instruction provides ahigh-performance means of generating pseudorandom numbers, meets theNIST standards, and is extendable to alternate generation techniques.The right-to-left processing of the instruction (e.g., in the generateoperation) offers certain performance advantages since, for instance,certain information need not be saved.

In one example, the instruction is extendable by specifying additionalfunction codes, each of which corresponds to a different algorithm usedto perform the initiation, reseeding and/or generation. The differentalgorithms may include other algorithms to meet NIST standards. Examplesof other algorithms include HMAC_DRBG (Hash-based Message AuthenticationCode DRBG), CTR_DRBG (Counter-DRBG), and DUAL_EC_DRBG(Dual_Elliptic_Curve_DRBG). Further, the function codes may be used toidentify different hash or key lengths, such as 512, 256, or others.Thus, in one example, the function code includes an indication of analgorithm and an indication of hash or key length, which provides manypossibilities aside from the SHA-512 technique described herein.Further, the function codes can specify other types of functions. Manypossibilities exist.

Herein, memory, main memory, storage and main storage are usedinterchangeably, unless otherwise noted explicitly or by context.

As will be appreciated by one skilled in the art, aspects may beembodied as a system, method or computer program product. Accordingly,aspects may take the form of an entirely hardware embodiment, anentirely software embodiment (including firmware, resident software,micro-code, etc.) or an embodiment combining software and hardwareaspects that may all generally be referred to herein as a “circuit,”“module” or “system”. Furthermore, aspects may take the form of acomputer program product embodied in one or more computer readablemedium(s) having computer readable program code embodied thereon.

Any combination of one or more computer readable medium(s) may beutilized. The computer readable medium may be a computer readablestorage medium. A computer readable storage medium may be, for example,but not limited to, an electronic, magnetic, optical, electromagnetic,infrared or semiconductor system, apparatus, or device, or any suitablecombination of the foregoing. More specific examples (a non-exhaustivelist) of the computer readable storage medium include the following: anelectrical connection having one or more wires, a portable computerdiskette, a hard disk, a random access memory (RAM), a read-only memory(ROM), an erasable programmable read-only memory (EPROM or Flashmemory), an optical fiber, a portable compact disc read-only memory(CD-ROM), an optical storage device, a magnetic storage device, or anysuitable combination of the foregoing. In the context of this document,a computer readable storage medium may be any tangible medium that cancontain or store a program for use by or in connection with aninstruction execution system, apparatus, or device.

Referring now to FIG. 10, in one example, a computer program product1000 includes, for instance, one or more non-transitory computerreadable storage media 1002 to store computer readable program codemeans or logic 1004 thereon to provide and facilitate one or moreaspects.

Program code embodied on a computer readable medium may be transmittedusing an appropriate medium, including but not limited to, wireless,wireline, optical fiber cable, RF, etc., or any suitable combination ofthe foregoing.

Computer program code for carrying out operations for aspects may bewritten in any combination of one or more programming languages,including an object oriented programming language, such as JAVA,Smalltalk, C++ or the like, and conventional procedural programminglanguages, such as the “C” programming language, assembler or similarprogramming languages. The program code may execute entirely on theuser's computer, partly on the user's computer, as a stand-alonesoftware package, partly on the user's computer and partly on a remotecomputer or entirely on the remote computer or server. In the latterscenario, the remote computer may be connected to the user's computerthrough any type of network, including a local area network (LAN) or awide area network (WAN), or the connection may be made to an externalcomputer (for example, through the Internet using an Internet ServiceProvider).

Aspects are described herein with reference to flowchart illustrationsand/or block diagrams of methods, apparatus (systems) and computerprogram products according to one or more embodiments. It will beunderstood that each block of the flowchart illustrations and/or blockdiagrams, and combinations of blocks in the flowchart illustrationsand/or block diagrams, can be implemented by computer programinstructions. These computer program instructions may be provided to aprocessor of a general purpose computer, special purpose computer, orother programmable data processing apparatus to produce a machine, suchthat the instructions, which execute via the processor of the computeror other programmable data processing apparatus, create means forimplementing the functions/acts specified in the flowchart and/or blockdiagram block or blocks.

These computer program instructions may also be stored in a computerreadable medium that can direct a computer, other programmable dataprocessing apparatus, or other devices to function in a particularmanner, such that the instructions stored in the computer readablemedium produce an article of manufacture including instructions whichimplement the function/act specified in the flowchart and/or blockdiagram block or blocks.

The computer program instructions may also be loaded onto a computer,other programmable data processing apparatus, or other devices to causea series of operational steps to be performed on the computer, otherprogrammable apparatus or other devices to produce a computerimplemented process such that the instructions which execute on thecomputer or other programmable apparatus provide processes forimplementing the functions/acts specified in the flowchart and/or blockdiagram block or blocks.

The flowchart and block diagrams in the figures illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods and computer program products according to variousembodiments. In this regard, each block in the flowchart or blockdiagrams may represent a module, segment, or portion of code, whichcomprises one or more executable instructions for implementing thespecified logical function(s). It should also be noted that, in somealternative implementations, the functions noted in the block may occurout of the order noted in the figures. For example, two blocks shown insuccession may, in fact, be executed substantially concurrently, or theblocks may sometimes be executed in the reverse order, depending uponthe functionality involved. It will also be noted that each block of theblock diagrams and/or flowchart illustration, and combinations of blocksin the block diagrams and/or flowchart illustration, can be implementedby special purpose hardware-based systems that perform the specifiedfunctions or acts, or combinations of special purpose hardware andcomputer instructions.

In addition to the above, one or more aspects may be provided, offered,deployed, managed, serviced, etc. by a service provider who offersmanagement of customer environments. For instance, the service providercan create, maintain, support, etc. computer code and/or a computerinfrastructure that performs one or more aspects for one or morecustomers. In return, the service provider may receive payment from thecustomer under a subscription and/or fee agreement, as examples.Additionally or alternatively, the service provider may receive paymentfrom the sale of advertising content to one or more third parties.

In one aspect, an application may be deployed for performing one or moreaspects. As one example, the deploying of an application comprisesproviding computer infrastructure operable to perform one or moreaspects.

As a further aspect, a computing infrastructure may be deployedcomprising integrating computer readable code into a computing system,in which the code in combination with the computing system is capable ofperforming one or more aspects.

As yet a further aspect, a process for integrating computinginfrastructure comprising integrating computer readable code into acomputer system may be provided. The computer system comprises acomputer readable medium, in which the computer medium comprises one ormore aspects. The code in combination with the computer system iscapable of performing one or more aspects.

Although various embodiments are described above, these are onlyexamples. For example, computing environments of other architectures canincorporate and use one or more aspects. Further, changes to theinstructions may be made without departing from the one or more aspects.Moreover, other registers may be used. Additionally, in otherembodiments (e.g., for other techniques), other values may be used inthe concatenations or other computations. Other variations are alsopossible.

Further, other types of computing environments can benefit from one ormore aspects. As an example, a data processing system suitable forstoring and/or executing program code is usable that includes at leasttwo processors coupled directly or indirectly to memory elements througha system bus. The memory elements include, for instance, local memoryemployed during actual execution of the program code, bulk storage, andcache memory which provide temporary storage of at least some programcode in order to reduce the number of times code must be retrieved frombulk storage during execution.

Input/Output or I/O devices (including, but not limited to, keyboards,displays, pointing devices, DASD, tape, CDs, DVDs, thumb drives andother memory media, etc.) can be coupled to the system either directlyor through intervening I/O controllers. Network adapters may also becoupled to the system to enable the data processing system to becomecoupled to other data processing systems or remote printers or storagedevices through intervening private or public networks. Modems, cablemodems, and Ethernet cards are just a few of the available types ofnetwork adapters.

Referring to FIG. 11, representative components of a Host Computersystem 5000 to implement one or more aspects are portrayed. Therepresentative host computer 5000 comprises one or more CPUs 5001 incommunication with computer memory (i.e., central storage) 5002, as wellas I/O interfaces to storage media devices 5011 and networks 5010 forcommunicating with other computers or SANs and the like. The CPU 5001 iscompliant with an architecture having an architected instruction set andarchitected functionality. The CPU 5001 may have dynamic addresstranslation (DAT) 5003 for transforming program addresses (virtualaddresses) into real addresses of memory. A DAT typically includes atranslation lookaside buffer (TLB) 5007 for caching translations so thatlater accesses to the block of computer memory 5002 do not require thedelay of address translation. Typically, a cache 5009 is employedbetween computer memory 5002 and the processor 5001. The cache 5009 maybe hierarchical having a large cache available to more than one CPU andsmaller, faster (lower level) caches between the large cache and eachCPU. In some implementations, the lower level caches are split toprovide separate low level caches for instruction fetching and dataaccesses. In one embodiment, an instruction is fetched from memory 5002by an instruction fetch unit 5004 via a cache 5009. The instruction isdecoded in an instruction decode unit 5006 and dispatched (with otherinstructions in some embodiments) to instruction execution unit or units5008. Typically several execution units 5008 are employed, for examplean arithmetic execution unit, a floating point execution unit and abranch instruction execution unit. The instruction is executed by theexecution unit, accessing operands from instruction specified registersor memory as needed. If an operand is to be accessed (loaded or stored)from memory 5002, a load/store unit 5005 typically handles the accessunder control of the instruction being executed. Instructions may beexecuted in hardware circuits or in internal microcode (firmware) or bya combination of both.

As noted, a computer system includes information in local (or main)storage, as well as addressing, protection, and reference and changerecording. Some aspects of addressing include the format of addresses,the concept of address spaces, the various types of addresses, and themanner in which one type of address is translated to another type ofaddress. Some of main storage includes permanently assigned storagelocations. Main storage provides the system with directly addressablefast-access storage of data. Both data and programs are to be loadedinto main storage (from input devices) before they can be processed.

Main storage may include one or more smaller, faster-access bufferstorages, sometimes called caches. A cache is typically physicallyassociated with a CPU or an I/O processor. The effects, except onperformance, of the physical construction and use of distinct storagemedia are generally not observable by the program.

Separate caches may be maintained for instructions and for dataoperands. Information within a cache is maintained in contiguous byteson an integral boundary called a cache block or cache line (or line, forshort). A model may provide an EXTRACT CACHE ATTRIBUTE instruction whichreturns the size of a cache line in bytes. A model may also providePREFETCH DATA and PREFETCH DATA RELATIVE LONG instructions which effectsthe prefetching of storage into the data or instruction cache or thereleasing of data from the cache.

Storage is viewed as a long horizontal string of bits. For mostoperations, accesses to storage proceed in a left-to-right sequence. Thestring of bits is subdivided into units of eight bits. An eight-bit unitis called a byte, which is the basic building block of all informationformats. Each byte location in storage is identified by a uniquenonnegative integer, which is the address of that byte location or,simply, the byte address. Adjacent byte locations have consecutiveaddresses, starting with 0 on the left and proceeding in a left-to-rightsequence. Addresses are unsigned binary integers and are 24, 31, or 64bits.

Information is transmitted between storage and a CPU or a channelsubsystem one byte, or a group of bytes, at a time. Unless otherwisespecified, in, for instance, the z/Architecture, a group of bytes instorage is addressed by the leftmost byte of the group. The number ofbytes in the group is either implied or explicitly specified by theoperation to be performed. When used in a CPU operation, a group ofbytes is called a field. Within each group of bytes, in, for instance,the z/Architecture, bits are numbered in a left-to-right sequence. Inthe z/Architecture, the leftmost bits are sometimes referred to as the“high-order” bits and the rightmost bits as the “low-order” bits. Bitnumbers are not storage addresses, however. Only bytes can be addressed.To operate on individual bits of a byte in storage, the entire byte isaccessed. The bits in a byte are numbered 0 through 7, from left toright (in, e.g., the z/Architecture). The bits in an address may benumbered 8-31 or 40-63 for 24-bit addresses, or 1-31 or 33-63 for 31-bitaddresses; they are numbered 0-63 for 64-bit addresses. Within any otherfixed-length format of multiple bytes, the bits making up the format areconsecutively numbered starting from 0. For purposes of error detection,and in preferably for correction, one or more check bits may betransmitted with each byte or with a group of bytes. Such check bits aregenerated automatically by the machine and cannot be directly controlledby the program. Storage capacities are expressed in number of bytes.When the length of a storage-operand field is implied by the operationcode of an instruction, the field is said to have a fixed length, whichcan be one, two, four, eight, or sixteen bytes. Larger fields may beimplied for some instructions. When the length of a storage-operandfield is not implied but is stated explicitly, the field is said to havea variable length. Variable-length operands can vary in length byincrements of one byte (or with some instructions, in multiples of twobytes or other multiples). When information is placed in storage, thecontents of only those byte locations are replaced that are included inthe designated field, even though the width of the physical path tostorage may be greater than the length of the field being stored.

Certain units of information are to be on an integral boundary instorage. A boundary is called integral for a unit of information whenits storage address is a multiple of the length of the unit in bytes.Special names are given to fields of 2, 4, 8, and 16 bytes on anintegral boundary. A halfword is a group of two consecutive bytes on atwo-byte boundary and is the basic building block of instructions. Aword is a group of four consecutive bytes on a four-byte boundary. Adoubleword is a group of eight consecutive bytes on an eight-byteboundary. A quadword is a group of 16 consecutive bytes on a 16-byteboundary. When storage addresses designate halfwords, words,doublewords, and quadwords, the binary representation of the addresscontains one, two, three, or four rightmost zero bits, respectively.Instructions are to be on two-byte integral boundaries. The storageoperands of most instructions do not have boundary-alignmentrequirements.

On devices that implement separate caches for instructions and dataoperands, a significant delay may be experienced if the program storesinto a cache line from which instructions are subsequently fetched,regardless of whether the store alters the instructions that aresubsequently fetched.

In one embodiment, the invention may be practiced by software (sometimesreferred to licensed internal code, firmware, micro-code, milli-code,pico-code and the like, any of which would be consistent with one ormore aspects). Referring to FIG. 11, software program code whichembodies one or more aspects may be accessed by processor 5001 of thehost system 5000 from long-term storage media devices 5011, such as aCD-ROM drive, tape drive or hard drive. The software program code may beembodied on any of a variety of known media for use with a dataprocessing system, such as a diskette, hard drive, or CD-ROM. The codemay be distributed on such media, or may be distributed to users fromcomputer memory 5002 or storage of one computer system over a network5010 to other computer systems for use by users of such other systems.

The software program code includes an operating system which controlsthe function and interaction of the various computer components and oneor more application programs. Program code is normally paged fromstorage media device 5011 to the relatively higher-speed computerstorage 5002 where it is available for processing by processor 5001. Thetechniques and methods for embodying software program code in memory, onphysical media, and/or distributing software code via networks are wellknown and will not be further discussed herein. Program code, whencreated and stored on a tangible medium (including but not limited toelectronic memory modules (RAM), flash memory, Compact Discs (CDs),DVDs, Magnetic Tape and the like is often referred to as a “computerprogram product”. The computer program product medium is typicallyreadable by a processing circuit preferably in a computer system forexecution by the processing circuit.

FIG. 12 illustrates a representative workstation or server hardwaresystem in which one or more aspects may be practiced. The system 5020 ofFIG. 12 comprises a representative base computer system 5021, such as apersonal computer, a workstation or a server, including optionalperipheral devices. The base computer system 5021 includes one or moreprocessors 5026 and a bus employed to connect and enable communicationbetween the processor(s) 5026 and the other components of the system5021 in accordance with known techniques. The bus connects the processor5026 to memory 5025 and long-term storage 5027 which can include a harddrive (including any of magnetic media, CD, DVD and Flash Memory forexample) or a tape drive for example. The system 5021 might also includea user interface adapter, which connects the microprocessor 5026 via thebus to one or more interface devices, such as a keyboard 5024, a mouse5023, a printer/scanner 5030 and/or other interface devices, which canbe any user interface device, such as a touch sensitive screen,digitized entry pad, etc. The bus also connects a display device 5022,such as an LCD screen or monitor, to the microprocessor 5026 via adisplay adapter.

The system 5021 may communicate with other computers or networks ofcomputers by way of a network adapter capable of communicating 5028 witha network 5029. Example network adapters are communications channels,token ring, Ethernet or modems. Alternatively, the system 5021 maycommunicate using a wireless interface, such as a CDPD (cellular digitalpacket data) card. The system 5021 may be associated with such othercomputers in a Local Area Network (LAN) or a Wide Area Network (WAN), orthe system 5021 can be a client in a client/server arrangement withanother computer, etc. All of these configurations, as well as theappropriate communications hardware and software, are known in the art.

FIG. 13 illustrates a data processing network 5040 in which one or moreaspects may be practiced. The data processing network 5040 may include aplurality of individual networks, such as a wireless network and a wirednetwork, each of which may include a plurality of individualworkstations 5041, 5042, 5043, 5044. Additionally, as those skilled inthe art will appreciate, one or more LANs may be included, where a LANmay comprise a plurality of intelligent workstations coupled to a hostprocessor.

Still referring to FIG. 13, the networks may also include mainframecomputers or servers, such as a gateway computer (client server 5046) orapplication server (remote server 5048 which may access a datarepository and may also be accessed directly from a workstation 5045). Agateway computer 5046 serves as a point of entry into each individualnetwork. A gateway is needed when connecting one networking protocol toanother. The gateway 5046 may be preferably coupled to another network(the Internet 5047 for example) by means of a communications link. Thegateway 5046 may also be directly coupled to one or more workstations5041, 5042, 5043, 5044 using a communications link. The gateway computermay be implemented utilizing an IBM eServer™ System z server availablefrom International Business Machines Corporation.

Referring concurrently to FIG. 12 and FIG. 13, software programming codewhich may embody one or more aspects of the present invention may beaccessed by the processor 5026 of the system 5020 from long-term storagemedia 5027, such as a CD-ROM drive or hard drive. The softwareprogramming code may be embodied on any of a variety of known media foruse with a data processing system, such as a diskette, hard drive, orCD-ROM. The code may be distributed on such media, or may be distributedto users 5050, 5051 from the memory or storage of one computer systemover a network to other computer systems for use by users of such othersystems.

Alternatively, the programming code may be embodied in the memory 5025,and accessed by the processor 5026 using the processor bus. Suchprogramming code includes an operating system which controls thefunction and interaction of the various computer components and one ormore application programs 5032. Program code is normally paged fromstorage media 5027 to high-speed memory 5025 where it is available forprocessing by the processor 5026. The techniques and methods forembodying software programming code in memory, on physical media, and/ordistributing software code via networks are well known and will not befurther discussed herein. Program code, when created and stored on atangible medium (including but not limited to electronic memory modules(RAM), flash memory, Compact Discs (CDs), DVDs, Magnetic Tape and thelike is often referred to as a “computer program product”. The computerprogram product medium is typically readable by a processing circuitpreferably in a computer system for execution by the processing circuit.

The cache that is most readily available to the processor (normallyfaster and smaller than other caches of the processor) is the lowest (L1or level one) cache and main store (main memory) is the highest levelcache (L3 if there are 3 levels). The lowest level cache is oftendivided into an instruction cache (I-Cache) holding machine instructionsto be executed and a data cache (D-Cache) holding data operands.

Referring to FIG. 14, an exemplary processor embodiment is depicted forprocessor 5026. Typically one or more levels of cache 5053 are employedto buffer memory blocks in order to improve processor performance. Thecache 5053 is a high speed buffer holding cache lines of memory datathat are likely to be used. Typical cache lines are 64, 128 or 256 bytesof memory data. Separate caches are often employed for cachinginstructions than for caching data. Cache coherence (synchronization ofcopies of lines in memory and the caches) is often provided by various“snoop” algorithms well known in the art. Main memory storage 5025 of aprocessor system is often referred to as a cache. In a processor systemhaving 4 levels of cache 5053, main storage 5025 is sometimes referredto as the level 5 (L5) cache since it is typically faster and only holdsa portion of the non-volatile storage (DASD, tape etc) that is availableto a computer system. Main storage 5025 “caches” pages of data paged inand out of the main storage 5025 by the operating system.

A program counter (instruction counter) 5061 keeps track of the addressof the current instruction to be executed. A program counter in az/Architecture processor is 64 bits and can be truncated to 31 or 24bits to support prior addressing limits. A program counter is typicallyembodied in a PSW (program status word) of a computer such that itpersists during context switching. Thus, a program in progress, having aprogram counter value, may be interrupted by, for example, the operatingsystem (context switch from the program environment to the operatingsystem environment). The PSW of the program maintains the programcounter value while the program is not active, and the program counter(in the PSW) of the operating system is used while the operating systemis executing. Typically, the program counter is incremented by an amountequal to the number of bytes of the current instruction. RISC (ReducedInstruction Set Computing) instructions are typically fixed length whileCISC (Complex Instruction Set Computing) instructions are typicallyvariable length. Instructions of the IBM z/Architecture are CISCinstructions having a length of 2, 4 or 6 bytes. The Program counter5061 is modified by either a context switch operation or a branch takenoperation of a branch instruction for example. In a context switchoperation, the current program counter value is saved in the programstatus word along with other state information about the program beingexecuted (such as condition codes), and a new program counter value isloaded pointing to an instruction of a new program module to beexecuted. A branch taken operation is performed in order to permit theprogram to make decisions or loop within the program by loading theresult of the branch instruction into the program counter 5061.

Typically an instruction fetch unit 5055 is employed to fetchinstructions on behalf of the processor 5026. The fetch unit eitherfetches “next sequential instructions”, target instructions of branchtaken instructions, or first instructions of a program following acontext switch. Modern Instruction fetch units often employ prefetchtechniques to speculatively prefetch instructions based on thelikelihood that the prefetched instructions might be used. For example,a fetch unit may fetch 16 bytes of instruction that includes the nextsequential instruction and additional bytes of further sequentialinstructions.

The fetched instructions are then executed by the processor 5026. In anembodiment, the fetched instruction(s) are passed to a dispatch unit5056 of the fetch unit. The dispatch unit decodes the instruction(s) andforwards information about the decoded instruction(s) to appropriateunits 5057, 5058, 5060. An execution unit 5057 will typically receiveinformation about decoded arithmetic instructions from the instructionfetch unit 5055 and will perform arithmetic operations on operandsaccording to the opcode of the instruction. Operands are provided to theexecution unit 5057 preferably either from memory 5025, architectedregisters 5059 or from an immediate field of the instruction beingexecuted. Results of the execution, when stored, are stored either inmemory 5025, registers 5059 or in other machine hardware (such ascontrol registers, PSW registers and the like).

A processor 5026 typically has one or more units 5057, 5058, 5060 forexecuting the function of the instruction. Referring to FIG. 15A, anexecution unit 5057 may communicate with architected general registers5059, a decode/dispatch unit 5056, a load store unit 5060, and other5065 processor units by way of interfacing logic 5071. An execution unit5057 may employ several register circuits 5067, 5068, 5069 to holdinformation that the arithmetic logic unit (ALU) 5066 will operate on.The ALU performs arithmetic operations such as add, subtract, multiplyand divide as well as logical function such as and, or and exclusive-or(XOR), rotate and shift. Preferably the ALU supports specializedoperations that are design dependent. Other circuits may provide otherarchitected facilities 5072 including condition codes and recoverysupport logic for example. Typically the result of an ALU operation isheld in an output register circuit 5070 which can forward the result toa variety of other processing functions. There are many arrangements ofprocessor units, the present description is only intended to provide arepresentative understanding of one embodiment.

An ADD instruction for example would be executed in an execution unit5057 having arithmetic and logical functionality while a floating pointinstruction for example would be executed in a floating point executionhaving specialized floating point capability. Preferably, an executionunit operates on operands identified by an instruction by performing anopcode defined function on the operands. For example, an ADD instructionmay be executed by an execution unit 5057 on operands found in tworegisters 5059 identified by register fields of the instruction.

The execution unit 5057 performs the arithmetic addition on two operandsand stores the result in a third operand where the third operand may bea third register or one of the two source registers. The execution unitpreferably utilizes an Arithmetic Logic Unit (ALU) 5066 that is capableof performing a variety of logical functions such as Shift, Rotate, And,Or and XOR as well as a variety of algebraic functions including any ofadd, subtract, multiply, divide. Some ALUs 5066 are designed for scalaroperations and some for floating point. Data may be Big Endian (wherethe least significant byte is at the highest byte address) or LittleEndian (where the least significant byte is at the lowest byte address)depending on architecture. The IBM z/Architecture is Big Endian. Signedfields may be sign and magnitude, 1's complement or 2's complementdepending on architecture. A 2's complement number is advantageous inthat the ALU does not need to design a subtract capability since eithera negative value or a positive value in 2's complement requires only anaddition within the ALU. Numbers are commonly described in shorthand,where a 12 bit field defines an address of a 4,096 byte block and iscommonly described as a 4 Kbyte (Kilo-byte) block, for example.

Referring to FIG. 15B, branch instruction information for executing abranch instruction is typically sent to a branch unit 5058 which oftenemploys a branch prediction algorithm such as a branch history table5082 to predict the outcome of the branch before other conditionaloperations are complete. The target of the current branch instructionwill be fetched and speculatively executed before the conditionaloperations are complete. When the conditional operations are completedthe speculatively executed branch instructions are either completed ordiscarded based on the conditions of the conditional operation and thespeculated outcome. A typical branch instruction may test conditioncodes and branch to a target address if the condition codes meet thebranch requirement of the branch instruction, a target address may becalculated based on several numbers including ones found in registerfields or an immediate field of the instruction for example. The branchunit 5058 may employ an ALU 5074 having a plurality of input registercircuits 5075, 5076, 5077 and an output register circuit 5080. Thebranch unit 5058 may communicate with general registers 5059, decodedispatch unit 5056 or other circuits 5073, for example.

The execution of a group of instructions can be interrupted for avariety of reasons including a context switch initiated by an operatingsystem, a program exception or error causing a context switch, an I/Ointerruption signal causing a context switch or multi-threading activityof a plurality of programs (in a multi-threaded environment), forexample. Preferably a context switch action saves state informationabout a currently executing program and then loads state informationabout another program being invoked. State information may be saved inhardware registers or in memory for example. State informationpreferably comprises a program counter value pointing to a nextinstruction to be executed, condition codes, memory translationinformation and architected register content. A context switch activitycan be exercised by hardware circuits, application programs, operatingsystem programs or firmware code (microcode, pico-code or licensedinternal code (LIC)) alone or in combination.

A processor accesses operands according to instruction defined methods.The instruction may provide an immediate operand using the value of aportion of the instruction, may provide one or more register fieldsexplicitly pointing to either general purpose registers or specialpurpose registers (floating point registers for example). Theinstruction may utilize implied registers identified by an opcode fieldas operands. The instruction may utilize memory locations for operands.A memory location of an operand may be provided by a register, animmediate field, or a combination of registers and immediate field asexemplified by the z/Architecture long displacement facility wherein theinstruction defines a base register, an index register and an immediatefield (displacement field) that are added together to provide theaddress of the operand in memory for example. Location herein typicallyimplies a location in main memory (main storage) unless otherwiseindicated.

Referring to FIG. 15C, a processor accesses storage using a load/storeunit 5060. The load/store unit 5060 may perform a load operation byobtaining the address of the target operand in memory 5053 and loadingthe operand in a register 5059 or another memory 5053 location, or mayperform a store operation by obtaining the address of the target operandin memory 5053 and storing data obtained from a register 5059 or anothermemory 5053 location in the target operand location in memory 5053. Theload/store unit 5060 may be speculative and may access memory in asequence that is out-of-order relative to instruction sequence, howeverthe load/store unit 5060 is to maintain the appearance to programs thatinstructions were executed in order. A load/store unit 5060 maycommunicate with general registers 5059, decode/dispatch unit 5056,cache/memory interface 5053 or other elements 5083 and comprises variousregister circuits, ALUs 5085 and control logic 5090 to calculate storageaddresses and to provide pipeline sequencing to keep operationsin-order. Some operations may be out of order but the load/store unitprovides functionality to make the out of order operations to appear tothe program as having been performed in order, as is well known in theart.

Preferably addresses that an application program “sees” are oftenreferred to as virtual addresses. Virtual addresses are sometimesreferred to as “logical addresses” and “effective addresses”. Thesevirtual addresses are virtual in that they are redirected to physicalmemory location by one of a variety of dynamic address translation (DAT)technologies including, but not limited to, simply prefixing a virtualaddress with an offset value, translating the virtual address via one ormore translation tables, the translation tables preferably comprising atleast a segment table and a page table alone or in combination,preferably, the segment table having an entry pointing to the pagetable. In the z/Architecture, a hierarchy of translation is providedincluding a region first table, a region second table, a region thirdtable, a segment table and an optional page table. The performance ofthe address translation is often improved by utilizing a translationlookaside buffer (TLB) which comprises entries mapping a virtual addressto an associated physical memory location. The entries are created whenthe DAT translates a virtual address using the translation tables.Subsequent use of the virtual address can then utilize the entry of thefast TLB rather than the slow sequential translation table accesses. TLBcontent may be managed by a variety of replacement algorithms includingLRU (Least Recently used).

In the case where the processor is a processor of a multi-processorsystem, each processor has responsibility to keep shared resources, suchas I/O, caches, TLBs and memory, interlocked for coherency. Typically,“snoop” technologies will be utilized in maintaining cache coherency. Ina snoop environment, each cache line may be marked as being in any oneof a shared state, an exclusive state, a changed state, an invalid stateand the like in order to facilitate sharing.

I/O units 5054 (FIG. 14) provide the processor with means for attachingto peripheral devices including tape, disc, printers, displays, andnetworks for example. I/O units are often presented to the computerprogram by software drivers. In mainframes, such as the System z fromIBM®, channel adapters and open system adapters are I/O units of themainframe that provide the communications between the operating systemand peripheral devices.

Further, other types of computing environments can benefit from one ormore aspects. As an example, an environment may include an emulator(e.g., software or other emulation mechanisms), in which a particulararchitecture (including, for instance, instruction execution,architected functions, such as address translation, and architectedregisters) or a subset thereof is emulated (e.g., on a native computersystem having a processor and memory). In such an environment, one ormore emulation functions of the emulator can implement one or moreaspects of the present invention, even though a computer executing theemulator may have a different architecture than the capabilities beingemulated. As one example, in emulation mode, the specific instruction oroperation being emulated is decoded, and an appropriate emulationfunction is built to implement the individual instruction or operation.

In an emulation environment, a host computer includes, for instance, amemory to store instructions and data; an instruction fetch unit tofetch instructions from memory and to optionally, provide localbuffering for the fetched instruction; an instruction decode unit toreceive the fetched instructions and to determine the type ofinstructions that have been fetched; and an instruction execution unitto execute the instructions. Execution may include loading data into aregister from memory; storing data back to memory from a register; orperforming some type of arithmetic or logical operation, as determinedby the decode unit. In one example, each unit is implemented insoftware. For instance, the operations being performed by the units areimplemented as one or more subroutines within emulator software.

More particularly, in a mainframe, architected machine instructions areused by programmers, usually today “C” programmers, often by way of acompiler application. These instructions stored in the storage mediummay be executed natively in a z/Architecture IBM® Server, oralternatively in machines executing other architectures. They can beemulated in the existing and in future IBM® mainframe servers and onother machines of IBM® (e.g., Power Systems servers and System X®Servers). They can be executed in machines running Linux on a widevariety of machines using hardware manufactured by IBM®, Intel®, AMD™,and others. Besides execution on that hardware under a z/Architecture,Linux can be used as well as machines which use emulation by Hercules,UMX, or FSI (Fundamental Software, Inc), where generally execution is inan emulation mode. In emulation mode, emulation software is executed bya native processor to emulate the architecture of an emulated processor.

The native processor typically executes emulation software comprisingeither firmware or a native operating system to perform emulation of theemulated processor. The emulation software is responsible for fetchingand executing instructions of the emulated processor architecture. Theemulation software maintains an emulated program counter to keep trackof instruction boundaries. The emulation software may fetch one or moreemulated machine instructions at a time and convert the one or moreemulated machine instructions to a corresponding group of native machineinstructions for execution by the native processor. These convertedinstructions may be cached such that a faster conversion can beaccomplished. Notwithstanding, the emulation software is to maintain thearchitecture rules of the emulated processor architecture so as toassure operating systems and applications written for the emulatedprocessor operate correctly. Furthermore, the emulation software is toprovide resources identified by the emulated processor architectureincluding, but not limited to, control registers, general purposeregisters, floating point registers, dynamic address translationfunction including segment tables and page tables for example, interruptmechanisms, context switch mechanisms, Time of Day (TOD) clocks andarchitected interfaces to I/O subsystems such that an operating systemor an application program designed to run on the emulated processor, canbe run on the native processor having the emulation software.

A specific instruction being emulated is decoded, and a subroutine iscalled to perform the function of the individual instruction. Anemulation software function emulating a function of an emulatedprocessor is implemented, for example, in a “C” subroutine or driver, orsome other method of providing a driver for the specific hardware aswill be within the skill of those in the art after understanding thedescription of one or more embodiments. Various software and hardwareemulation patents including, but not limited to U.S. Pat. No. 5,551,013,entitled “Multiprocessor for Hardware Emulation”, by Beausoleil et al.;and U.S. Pat. No. 6,009,261, entitled “Preprocessing of Stored TargetRoutines for Emulating Incompatible Instructions on a Target Processor”,by Scalzi et al; and U.S. Pat. No. 5,574,873, entitled “Decoding GuestInstruction to Directly Access Emulation Routines that Emulate the GuestInstructions”, by Davidian et al; and U.S. Pat. No. 6,308,255, entitled“Symmetrical Multiprocessing Bus and Chipset Used for CoprocessorSupport Allowing Non-Native Code to Run in a System”, by Gorishek et al;and U.S. Pat. No. 6,463,582, entitled “Dynamic Optimizing Object CodeTranslator for Architecture Emulation and Dynamic Optimizing Object CodeTranslation Method”, by Lethin et al; and U.S. Pat. No. 5,790,825,entitled “Method for Emulating Guest Instructions on a Host ComputerThrough Dynamic Recompilation of Host Instructions”, by Eric Traut, eachof which is hereby incorporated herein by reference in its entirety; andmany others, illustrate a variety of known ways to achieve emulation ofan instruction format architected for a different machine for a targetmachine available to those skilled in the art.

In FIG. 16, an example of an emulated host computer system 5092 isprovided that emulates a host computer system 5000′ of a hostarchitecture. In the emulated host computer system 5092, the hostprocessor (CPU) 5091 is an emulated host processor (or virtual hostprocessor) and comprises an emulation processor 5093 having a differentnative instruction set architecture than that of the processor 5091 ofthe host computer 5000′. The emulated host computer system 5092 hasmemory 5094 accessible to the emulation processor 5093. In the exampleembodiment, the memory 5094 is partitioned into a host computer memory5096 portion and an emulation routines 5097 portion. The host computermemory 5096 is available to programs of the emulated host computer 5092according to host computer architecture. The emulation processor 5093executes native instructions of an architected instruction set of anarchitecture other than that of the emulated processor 5091, the nativeinstructions obtained from emulation routines memory 5097, and mayaccess a host instruction for execution from a program in host computermemory 5096 by employing one or more instruction(s) obtained in asequence & access/decode routine which may decode the hostinstruction(s) accessed to determine a native instruction executionroutine for emulating the function of the host instruction accessed.Other facilities that are defined for the host computer system 5000′architecture may be emulated by architected facilities routines,including such facilities as general purpose registers, controlregisters, dynamic address translation and I/O subsystem support andprocessor cache, for example. The emulation routines may also takeadvantage of functions available in the emulation processor 5093 (suchas general registers and dynamic translation of virtual addresses) toimprove performance of the emulation routines. Special hardware andoff-load engines may also be provided to assist the processor 5093 inemulating the function of the host computer 5000′.

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of the invention. Asused herein, the singular forms “a”, “an” and “the” are intended toinclude the plural forms as well, unless the context clearly indicatesotherwise. It will be further understood that the terms “comprises”and/or “comprising”, when used in this specification, specify thepresence of stated features, integers, steps, operations, elements,and/or components, but do not preclude the presence or addition of oneor more other features, integers, steps, operations, elements,components and/or groups thereof

The corresponding structures, materials, acts, and equivalents of allmeans or step plus function elements in the claims below, if any, areintended to include any structure, material, or act for performing thefunction in combination with other claimed elements as specificallyclaimed. The description of one or more aspects has been presented forpurposes of illustration and description, but is not intended to beexhaustive or limited to the invention in the form disclosed. Manymodifications and variations will be apparent to those of ordinary skillin the art without departing from the scope and spirit of one or moreaspects. The embodiment was chosen and described in order to bestexplain the principles of the one or more aspects and the practicalapplication, and to enable others of ordinary skill in the art tounderstand the one or more aspects for various embodiments with variousmodifications as are suited to the particular use contemplated.

What is claimed is:
 1. A computer program product for executing amachine instruction, the computer program product comprising: anon-transitory computer readable storage medium readable by a processingcircuit and storing instructions for execution by the processing circuitfor performing a method comprising: obtaining, by a processor, a machineinstruction for execution, the machine instruction being defined forcomputer execution according to a computer architecture, the machineinstruction comprising: an opcode field to provide an opcode, the opcodeto identify a perform pseudorandom number operation; and a registerfield to be used to identify a register, the register to specify alocation in memory of a second operand to be used by the machineinstruction; and executing the machine instruction, the executingcomprising: obtaining a modifier (M) field of a register associated withthe machine instruction; based on the M field having a first value,performing a deterministic pseudorandom number seed operation, thedeterministic pseudorandom number seed operation comprising: obtainingseed material based on information included in the second operand; usinga 512 bit secure hash technique and the seed material to provide one ormore seed values; and storing the one or more seed values in a parameterblock associated with the machine instruction.
 2. The computer programproduct of claim 1, wherein the machine instruction further comprisesanother register field to be used to identify another register, theanother register to specify a location in memory of a first operand tobe used by the machine instruction, and wherein the method furthercomprises: executing the machine instruction another time, the executingthe machine instruction another time comprising: based on the M fieldhaving a second value, performing a deterministic pseudorandom numbergenerate operation, the deterministic pseudorandom number generateoperation comprising: for each block of memory of one or more blocks ofmemory of the first operand, generating a hash value using the 512 bitsecure hash technique and at least one seed value of the one or moreseed values in the parameter block, and storing at least a portion ofthe generated hash value in a corresponding block of memory of the firstoperand, the generated hash value being at least a portion of apseudorandom number.
 3. The computer program product of claim 1, whereinthe executing further comprises obtaining a function code from theregister associated with the machine instruction, the function code tospecify a function to be performed, and based on the function code beinga particular value, obtaining the modifier field, and wherein theparameter block is located using another register associated with themachine instruction.
 4. The computer program product of claim 1, whereinthe parameter block is configured to include a reseed counter toindicate a number of times the machine instruction has completed with aspecific condition code since the parameter block was last instantiatedor reseeded; a stream bytes field to track a number of bytes storedbased on a generate operation; a value to indicate an internal state ofa random number generator represented by the parameter block; and aconstant value to be initialized by execution of a seed operation. 5.The computer program product of claim 1, wherein the deterministicpseudorandom number seed operation further comprises forming the seedmaterial, the forming based on a value of a reseed counter of theparameter block.
 6. The computer program product of claim 5, whereinbased on the value of the reseed counter having one value, the formingcomprises using the information of the second operand to form the seedmaterial, the information comprising at least one of entropy input,nonce and a personalized string.
 7. The computer program product ofclaim 5, wherein based on the value of the reseed counter having anothervalue, the forming comprises combining a selected value, contents of avalue field of the parameter block, and the information of the secondoperand to form the seed material, the information comprising at leastone of entropy input and additional input.
 8. The computer programproduct of claim 1, wherein the using the 512 bit secure hash techniqueto provide one or more seed values comprises using the 512 bit securehash technique to provide a V_(new) seed value, the using to provide theV_(new) seed value comprising: providing a first counter, a selectedvalue, the seed material and padding to the 512 bit secure hashtechnique; invoking the 512 bit secure hash technique using the firstcounter, the selected value, the seed material and the padding to obtaina first hashed result; providing a second counter, the selected value,the seed material and the padding to the 512 bit secure hash technique;invoking the 512 bit secure hash technique using the second counter, theselected value, the seed material and the padding to obtain a secondhashed result; combining the first hashed result and the second hashedresult to obtain a combined result; and using a portion of the combinedresult to provide the V_(new) seed value.
 9. The computer programproduct of claim 8, wherein the using the 512 bit secure hash techniqueto provide the one or more seed values further comprises using the 512bit secure hash technique to provide a C_(new) seed value, the using toprovide the C_(new) seed value comprising: invoking the 512 bit securehash technique using the first counter, the selected value, a definedvalue, the V_(new) w seed value, and the padding to obtain a thirdhashed result; invoking the 512 bit secure hash technique using thesecond counter, the selected value, the defined value, the V_(new) seedvalue, and the padding to obtain a fourth hashed result; combining thethird hashed result and the fourth hashed result to obtain anothercombined result; and using a portion of the another combined result toprovide the C_(new) seed value.
 10. The computer program product ofclaim 9, wherein the combining the first hashed value and the secondhashed value comprises concatenating the first hashed value and thesecond hashed value to provide the combined result, and the using aportion of the combined result comprises using a leftmost number ofbytes of the combined result as V_(new); and wherein the combining thethird hashed value and the fourth hashed value comprises concatenatingthe third hashed value and the fourth hashed value to provide theanother combined result, and the using a portion of the another combinedresult comprises using a leftmost number of bytes of the anothercombined result as C_(new).
 11. A computer system for executing amachine instruction, the computer system comprising: a memory; and aprocessor in communications with the memory, wherein the computer systemis configured to perform a method, said method comprising: obtaining, bya processor, a machine instruction for execution, the machineinstruction being defined for computer execution according to a computerarchitecture, the machine instruction comprising: an opcode field toprovide an opcode, the opcode to identify a perform pseudorandom numberoperation; and a register field to be used to identify a register, theregister to specify a location in memory of a second operand to be usedby the machine instruction; and executing the machine instruction, theexecuting comprising: obtaining a modifier (M) field of a registerassociated with the machine instruction; based on the M field having afirst value, performing a deterministic pseudorandom number seedoperation, the deterministic pseudorandom number seed operationcomprising: obtaining seed material based on information included in thesecond operand; using a 512 bit secure hash technique and the seedmaterial to provide one or more seed values; and storing the one or moreseed values in a parameter block associated with the machineinstruction.
 12. The computer system of claim 11, wherein the machineinstruction further comprises another register field to be used toidentify another register, the another register to specify a location inmemory of a first operand to be used by the machine instruction, andwherein the method further comprises: executing the machine instructionanother time, the executing the machine instruction another timecomprising: based on the M field having a second value, performing adeterministic pseudorandom number generate operation, the deterministicpseudorandom number generate operation comprising: for each block ofmemory of one or more blocks of memory of the first operand, generatinga hash value using the 512 bit secure hash technique and at least oneseed value of the one or more seed values in the parameter block, andstoring at least a portion of the generated hash value in acorresponding block of memory of the first operand, the generated hashvalue being at least a portion of a pseudorandom number.
 13. Thecomputer system of claim 11, wherein the deterministic pseudorandomnumber seed operation further comprises forming the seed material, theforming based on a value of a reseed counter of the parameter block, andwherein based on the value of the reseed counter having one value, theforming comprises using the information of the second operand to formthe seed material, the information comprising at least one of entropyinput, nonce and a personalized string.
 14. The computer system of claim11, wherein the deterministic pseudorandom number seed operation furthercomprises forming the seed material, the forming based on a value of areseed counter of the parameter block, and wherein based on the value ofthe reseed counter having another value, the forming comprises combininga selected value, contents of a value field of the parameter block, andthe information of the second operand to form the seed material, theinformation comprising at least one of entropy input and additionalinput.
 15. The computer system of claim 11, wherein the using the 512bit secure hash technique to provide one or more seed values comprisesusing the 512 bit secure hash technique to provide a V_(new) seed value,the using to provide the V_(new) seed value comprising: providing afirst counter, a selected value, the seed material and padding to the512 bit secure hash technique; invoking the 512 bit secure hashtechnique using the first counter, the selected value, the seed materialand the padding to obtain a first hashed result; providing a secondcounter, the selected value, the seed material and the padding to the512 bit secure hash technique; invoking the 512 bit secure hashtechnique using the second counter, the selected value, the seedmaterial and the padding to obtain a second hashed result; combining thefirst hashed result and the second hashed result to obtain a combinedresult; and using a portion of the combined result to provide theV_(new) seed value.
 16. The computer system of claim 15, wherein theusing the 512 bit secure hash technique to provide the one or more seedvalues further comprises using the 512 bit secure hash technique toprovide a C_(new) seed value, the using to provide the C_(new) seedvalue comprising: invoking the 512 bit secure hash technique using thefirst counter, the selected value, a defined value, the V_(new) seedvalue, and the padding to obtain a third hashed result; invoking the 512bit secure hash technique using the second counter, the selected value,the defined value, the V_(new) seed value and the padding to obtain afourth hashed result; combining the third hashed result and the fourthhashed result to obtain another combined result; and using a portion ofthe another combined result to provide the C_(new) seed value.
 17. Thecomputer system of claim 16, wherein the combining the first hashedvalue and the second hashed value comprises concatenating the firsthashed value and the second hashed value to provide the combined result,and the using a portion of the combined result comprises using aleftmost number of bytes of the combined result as V_(new); and whereinthe combining the third hashed value and the fourth hashed valuecomprises concatenating the third hashed value and the fourth hashedvalue to provide the another combined result, and the using a portion ofthe another combined result comprises using a leftmost number of bytesof the another combined result as C_(new).